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arXiv · 1711.02561

Translatability and translatable semigroups

Wieslaw A. Dudek·Robert A. R. Monzo
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Abstract

The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatable groupoids are proved. Necessary and sufficient conditions are found for a left cancellative k-translatable groupoid to be a semigroup. Any such semigroup is proved to be left unitary and a union of disjoint copies of cyclic groups of the same order. Methods of constructing k-translatable semigroups that are not left cancellative are given.

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Wieslaw A. Dudek, Robert A. R. Monzo. 2017-11-06. Translatability and translatable semigroups. https://arxiv.org/abs/1711.02561

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